Howard Kendall, the manager of the First Division club, has been in touch with his Rangers counterpart, Walter Smith, about the controversial England midfield player, but refused to reveal whether he has tabled an offer.
"I can confirm I have spoken to Walter about Gascoigne, but what was discussed must remain private," Kendall said.
Sheffield United are looking to make a major signing ahead of their planned flotation on the Stock Exchange later this month. The scheme that will release millions of pounds to fund chairman Mike McDonald's grand design for the Blades.
However, Donald Findlay, the Rangers vice-chairman, said yesterday: "I know of no change in our policy to have Gascoigne honour his three-year contract."
Gascoigne, a club record pounds 4.3m purchase from Lazio in July 1995, is almost half-way through his existing deal with Rangers.
Smith declined to transfer-list the 29-year-old former Newcastle and Tottenham player, despite recent problems off the pitch with allegations of wife-beating, which he has not denied.
The England manager, Glenn Hoddle, also stuck by Gascoigne, who has been noticeably calmer in recent matches after starting counselling sessions.
With fellow-midfielder Stuart McCall sidelined by injury and Rangers three points ahead of Celtic in their attempt to equal their rivals' run of nine successive Scottish championships, selling Gascoigne would seem unlikely.
"We are in the middle of a very important season," Findlay said. "Nobody will be leaving Ibrox on the cheap, that is for sure, and certainly not any of our best players."
Gascoigne has been a success in a domestic context for Rangers scoring 30 goals in 58 appearances.Reuse content